The isosceles trapezoid is, in fact, a trapezoid (that is, a four-sided polygon with two of them - the bases - being parallel), with two of its sides being equivalent and with its base angles of equal magnitude.
The isosceles trapezoid is, in fact, a trapezoid (that is, a four-sided polygon with two of them - the bases - being parallel), with two of its sides being equivalent and with its base angles of equal magnitude.
In the trapezoid, as is known, there are two bases and, each base has two base angles adjacent on both sides. In other words, in the isosceles trapezoid, there are two sets of equal base angles, as can be seen in the following illustration:
\( ∢D=50° \)
The isosceles trapezoid
What is \( ∢B \)?
The isosceles trapezoid is, in fact, a trapezoid (that is, a four-sided polygon with two of them - the bases - being parallel), with two of its sides being equivalent and with its base angles of equal magnitude.
In the trapezoid, as is known, there are two bases and, each base has two adjacent base angles on both sides. In other words, in the isosceles trapezoid, there are two sets of equal base angles, as can be seen in the following illustration:
The properties detailed here are the unique characteristics of isosceles trapezoids among all other types of trapezoids. The following illustration describes the theorems in the best way:
That is, angles and are equivalent, just like angles and are also.
Given: \( ∢A=120° \)
The isosceles trapezoid
Find a: \( ∢C \)
Given: \( ∢C=2x \)
\( ∢A=120° \)
isosceles trapezoid.
Find x.
In all isosceles trapezoids the bases are equal?
To demonstrate that a trapezoid is isosceles, we must make use of the properties specified earlier, in fact, these are reciprocal theorems. It is sufficient to demonstrate just one property.
That is, if we prove that:
or
or
then, said trapezoid is an isosceles trapezoid.
The following properties refer to the diagonals of the isosceles trapezoid. To highlight these properties in the best way, we will use this illustration:
Do isosceles trapezoids have two pairs of parallel sides?
Look at the polygon in the diagram.
What type of shape is it?
Below is an isosceles trapezoid.
\( ∢B=3x \)
\( ∢D=x \)
Calculate the size of angle \( ∢B \).
The calculation of the area of an isosceles trapezoid is done exactly in the same way as the area of any other trapezoid is calculated.
That is, the lengths of the two bases are added, the total sum is multiplied by the height, and then, it is divided by .
We will use this illustration to explain the steps of the calculation:
The formula to calculate the area of the isosceles trapezoid (not exclusively) is:
Given the isosceles trapezoid described in the following scheme.
It is known that the sum of three angles is degrees.
According to the data, we must calculate all the angles of this isosceles trapezoid.
Solution:
If the sum of the three angles of the given trapezoid is and the total sum of the angles of a trapezoid (as with any quadrilateral) is , we can deduce that the fourth angle measures degrees.
It is one of the adjacent angles to the smaller base, let's assume angle . Since it is an isosceles trapezoid, the angles at the base are congruent, therefore, angle also measures .
Remember that it is a trapezoid and that the bases and are parallel, that is, angles and (just like and ) are collateral angles and, therefore, complement each other and together measure degrees. Therefore, it will give us that angles and measure degrees.
Answer:
The angles of the trapezoid are
In an isosceles trapezoid, will the sum of the opposite angles always be 180°?
Are the diagonals of an isosceles trapezoid equal and do they intersect each other?
Do the diagonals of the trapezoid necessarily cross each other?
Given the isosceles trapezoid described in the following scheme.
It is known that the sum of two of its sides is .
According to the data, we must calculate all the angles of this isosceles trapezoid.
Solution:
Let's go back to the rules related to the base and remember that it is a trapezoid and that the bases and are parallel, that is, the angles and (as well as and ) are collateral angles and, therefore, complement each other and together measure degrees. Given that the amplitude we have is degrees, we can deduce that these are not adjacent angles on the same side (i.e., unilateral), but angles that share the same base.
Being an isosceles trapezoid, the base angles are congruent, therefore, each of them measures degrees.
The complementary angle (to reach degrees) of each of these angles measures degrees.
Answer:
The angles of the trapezoid are
The perimeter of the trapezoid equals 22 cm.
AB = 7 cm
AC = 3 cm
BD = 3 cm
What is the length of side CD?
Given: \( ∢A=y+20 \)
\( ∢D=50 \)
trapecio isósceles.
Find a \( ∢A \)
Below is an isosceles trapezoid.
\( ∢B=2y+20 \)
\( ∢D=60 \)
Calculate the size of \( ∢B \).